+0

# 2017 NS 28

+1
30
9
+411

Can anyone solve this? (without calculator please) Answer: 0.25

Mar 14, 2019
edited by dgfgrafgdfge111  Mar 15, 2019

#1
+411
0

Here's what I tried:

First I looked at 1.75 + sqrt(3) and said, "Well, why not set it equal to a variable?". So I replaced it with x.

Then I got $$2\sqrt{x} - x$$, but that didn't help at all. I can't set it equal to anything. I can't solve it with a variable. So then I thought I would just need to solve it by hand. But how in the world would I know what $$\sqrt{3}$$ was? Luckily, I remebered that it was 1.732. So, thenI solved it as shown below:

$$2\sqrt{1.75+1.732} - (1.75+1.732)$$

$$=2\sqrt{3.482}-3.482$$

Now what? How do I solve this?

Mar 15, 2019
#3
+3994
+1

Try to square it. Do you think approximations would help?

tertre  Mar 15, 2019
#5
+411
0

If we squared it, though, we would get 2(sqrt(3.482)), which wouldn't simplify.

dgfgrafgdfge111  Mar 15, 2019
#6
+3994
+1

It actually gets around 0.2500002, so 0.25.

tertre  Mar 15, 2019
#7
+411
0

Did you use calc or use approximates?

dgfgrafgdfge111  Mar 15, 2019
#2
+99238
0

$$2\sqrt{1.75+\sqrt3}-(1.75+\sqrt3)\\$$

I'm coming up blank.

but   sqrt root of 3   is irrational so it is not exactly equal to what you said.

Mar 15, 2019
#4
+411
0

Yeah, I just approximated it.

dgfgrafgdfge111  Mar 15, 2019
#8
+99238
+2

Finally I got it !!

$$2\sqrt{1.75+\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{4(\frac{7}{4}+\sqrt3)}\qquad -(1.75+\sqrt3)\\~\\ =\sqrt{7+4\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2)^2+(2*2*\sqrt3)+(\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2+\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =(2+\sqrt3)\qquad-(1.75+\sqrt3)\\~\\ =2+\sqrt3-1.75-\sqrt3\\~\\ =0.25$$

Is that impressive or what!   LOL

Mar 15, 2019
#9
+411
+1

Wow, that's smart!!!!

dgfgrafgdfge111  Mar 15, 2019